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Modeling and pricing cyber insurance
The paper provides a comprehensive overview of modeling and pricing cyber insurance and includes clear and easily understandable explanations of the...
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Additive logistic processes in option pricing
In option pricing, it is customary to first specify a stochastic underlying model and then extract valuation equations from it. However, it is...
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Stochastic Volatility Models: Methods of Pricing, Hedging and Estimation
Stochastic volatility models are partially observed diffusions and are hidden Markov models when the driving noises are Brownian motions. The chapter...
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FFT-network for bivariate Lévy option pricing
We propose a two-dimensional fast Fourier transform (FFT) network to retrieve the prices of options that depend on two Lévy processes. Applications...
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Volatility Term Structure and Exotic Options
We describe arguably the most significant oil derivative trade, the large-scale annual put buying program by the Government of Mexico. The complexity...
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On Extension of the Markov Chain Approximation Method for Computing Feynman–Kac Type Expectations
An efficient discrete time and space Markov chain approximation employing a Brownian bridge correction for computing curvilinear boundary crossing...
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Volatility Arbitrage and Model Calibration
This chapter focuses on the important problem of model calibration. We present the bootstrap** method for calibrating volatility time-dependency...
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Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs
Physics-informed neural networks approximate solutions of PDEs by minimizing pointwise residuals. We derive rigorous bounds on the error, incurred by...
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On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models
In this paper we focus on qualitative properties of solutions to a nonlocal nonlinear partial integro-differential equation (PIDE). Using the theory...
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Combined Derivative Estimators
We discuss combinations of simulation-based derivative estimators using infinitesimal perturbation analysis (IPA) and the likelihood ratio method...
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Volatility Smile Trading
We study the problem of the volatility smile and the strategy of vega trading. We demonstrate limitations of conventional paradigms to the oil market...
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High Mathematics Meets High Finance
Mathematics in finance has prehistoric origins, in fact it is argued that an accounting system of clay tokens used for prehistoric commerce were...
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High Mathematics Meets High Finance
Mathematics in finance has prehistoric origins, in fact it is argued that an accounting system of clay tokens used for prehistoric commerce were...
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American option pricing under GARCH with non-normal innovations
As it is well known from the time-series literature, GARCH processes with non-normal shocks provide better descriptions of stock returns than GARCH...
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Quantization-Based Numerical Schemes
In this chapter we will present and analyze several spatial discretization schemes of an...
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On Incentive Compatibility in Dynamic Mechanism Design With Exit Option in a Markovian Environment
This paper studies dynamic mechanism design in a Markovian environment and analyzes a direct mechanism model of a principal-agent framework in which...
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Quantization Methods for Stochastic Differential Equations
In this paper we provide an introduction to quantization with applications in quantitative finance.We start with a review of vector quantization...
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The role of optimization in some recent advances in data-driven decision-making
Data-driven decision-making has garnered growing interest as a result of the increasing availability of data in recent years. With that growth many...
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Robust Chance-Constrained Geometric Programming with Application to Demand Risk Mitigation
We determine bounds on the optimal value for a chance-constrained program aiming to minimize the worst-case probability that a certain nonlinear...
